# Analysing Specific Capacity and Energy Density of some popular batteries

In my last article, I was concentrating more about the Specific Capacity of different cathode materials. But this is only one part of the story when a complete cell is concerned. To find the Specific Capacity of a particular battery chemistry the whole chemical reaction has to be analyzed.

Essentially the method used here is similar to that of previous analysis. Instead of just the cathode material, we have to consider the complete chemical reaction taking place in both cathode and anode. But the rest of the calculation is nearly the same. In short,
```Specific Capacity = (N x F) / (Total weight of all components) where, N = Change in oxidation state or the number of electrons released. F = Faraday constant, 26801mAh/Mole ```

This is one of the oldest rechargeable batteries invented, yet ubiquitous. The following is the chemical reaction happening in both Cathode and Anode during discharge process.
-ve Electrode: Cathode: Pb + H2SO4 = PbSO4 + 2H+ + 2e
+ve Electrode: PbO2 + H2SO4 + 2H+ = PbSO4 + 2H2O
The total chemical reaction is,
`Pb + PbO2 + 2 H2SO4 = 2 PbSO4 + 2H2O (with 2 electrons through circuit)`
Finding the total molar weight, 643g of reactants produce 2 Moles of electrons.``` Specific Capacity = 2 * 26.801/643 = 83mAh/g Total Energy Density, assuming 2V per reaction = 166 Wh/g ```

Lithium Ion (Lithium Ferrous Phosphate):
This is one of the variants in the family of Lithium Ion Battery.
Overall Chemical reaction during reaction is as follows
`LiC6 + FePO4 = LiFePO4 + 6C (with 1 electron through circuit)`
That means 230g of reactants produce 1 Mole of electrons, at 3.3V
Calculating both Specific Capacity and Energy Density
```Specific Capacity = 26.801/230 = 117mAh/g Energy Density = 385Wh/kg```

Sodium Sulphur:
Mainly used in grid scale energy storage application, Sodium Sulphur is a variant of molten metal battery.
To give the overall chemical reaction,
`2Na + 4S = Na2S4 (with 2 electrons through circuit)`
The cell gives out 2V.
In this case, 174g of reactants, give out 2 Mole of electrons.
So Specific Capacity and Energy Density are
```Specific Capacity = 308mAh/g Energy Density = 616Wh/kg```

Conclusion:
It could be easily seen that Lead Acid battery, even though most widely used has a very low theoretical capacity. An interesting finding is that, the current practical capacities of both Lithium-Ion and Sodium Sulphur batteries are reaching very near to the theoretical capacity of Lead Acid technology.